Split phase is just a single phase bipolar or normal/inverted polarity phase. Think of it like unbalanced vs balanced audio. It's the same signal. As others have said it's just a centre-tapped 240V system. rather than having 1 x 240V signal and 1 x Neutral signal you have 2 x 120V signals out of phase.
1ph is 1ph. No shift, no inversion.
Some see a flip because they flip the probes over (using C.tap as the gnd point).
Use one or two o-scopes and probes on a low voltage C.tap xfrmr (12vac w/ C.tap).
(isolated secondary w/ isolated scope inputs)
Probe1------GND
S1-----------C.tap----------S2
Probe2---------GND
Voltage only builds or reduces in one direction (vector) at any given time. Why? Because there's only one mag field vector.
When L1 reaches +6v, L2 is becomes -6v. end-end is 12v differential, end to tap is 6v.
People get tricked when they make C.tap the common for both probes, which make the 1ph look like inversion or 180 shift, it's not.
This setup(view) is deceiving, but is accurate in physics realm.
Probe1------GND
L1-----------C.tap----------L2
GND---------Probe2
Look at it carefully, notice the physical probe is physically flipped over 180deg.

For simple coil xfrmers, unless a mag field cuts coils (or tapped sections of one coil) at different times, then there can only be one phase. You also do not see 3ph on one wire, you must have three 1ph wires.
